Å General View of the Contents of this work.

THE System of Geometry is divided into two parts. The first contains Geometrical Definitions respecting Lines, Angles, Superficies, &c. The second part contains a number of Geometrical Problems necessary for Trigonometry and Surveying.

The System of Trigonometry is also divided into two parts; and teaches the solution of Questions in Right and Oblique angled Trigoremetry, by Logarithms and also by Natural Sines.

The Treatise on Surveying is divided into three parts. Part first treats of measuring Land, and is divided into three Sections. The first contains several Problems respecting Mensuration, and for finding the Area of various Right-lined Figures and Circles.

The second Section teaches different methods of taking the Survey of Fields; also to protract them, and find their Area in the manner commonly practised, .and likewise by Arithmetical and Trigonometrical calculations, without measuring Diagonals and Perpendiculars with a Scale and Dividers ; interspersed with sundry useful rules and directions.

The third Section is a particular explanation and demonstration of Rectangular Surveying, or the method of computing the Area of Fields from the Field Notes, by Mathematical Tables, without the necessity of plotting the Field. To this Section is added a use. ful Problem for ascertaining the true Area of a Field which has been measured. by a Chain too long or too

elements of Surveying upon a larger scale ; and the

system of Geometry and Trigonometry with which it

is introduced, with the Problems for the mensuration

of Superficies, as also the Mathematical Tables at the

end, will be found useful for many other

purposes. It

would be well, therefore, for those who do not intend

to become practical Surveyors, to acquaint themselves

with what is here taught ; and with this view the fol-

lowing work is very proper to be introduced into Acad.

emies, and those wigher Schools which are designed

to fit young men for active business in life. Indeed

every person who frequently buys and sells land should

learn to calculate the Contents of a Field Arithmetically ;

a knowledge which may be acquired in a very little

time, from the particular explanation here given of that

method.

Notwithstanding the many Books already published
on the subjects here treated upon, it was thought a work
of this kind was really wanted, and that if judiciously
executed it would be useful. It is more particularly
necessary at the present time in Connecticut, as the
Legislature of the State have lately enacted a Law on
the subject of Surveying, in consequence of which
more attention must be paid to the Theory of that Art
than has been common.

These considerations induced the Compiler to select
from various publications what appeared to him im-
portant; and to arrange the whole in a method best
adapted, in his view, for teaching that useful Art,
Ilow far he has succeeded in his endeavor to simplify
the subject, and render it easy to the Learner, must be
submitted to the test of experience.

Å General View of the Contents of this Work.

THE System of Geometry is divided into two parts.
The first contains Geometrical Definitions respecting
Lines, Angles, Superficies, &c. The second part con-
tains a number of Geometrical Problems necessary for
Trigonometry and Surveying.

The System of Trigonometry is also divided into
two parts ; and teaches the solution of Questions in
Right and Oblique angled Trigor metry, by Loga-
rithms and also by Natural Sines.

The Treatise on Surveying is divided into three
parts. Part first treats of measuring Land, and is di-
vided into three Sections. The first contains several
Problems respecting Mensúration, and for finding the
Area of various Right-lined Figures and Circles.

The second Section teaches different methods of
taking the Survey of Fields; also to protract them,
and find their Area in the manner commonly practised,
and likewise by Arithmetical and Trigonometrical cal-
culations, without measuring Diagonals and Perpen-
diculars with a Scale and Dividers; interspersed with
sundry useful rules and directions.

The third Section is a particular explanation and
demonstration of Rectangular Surveying, or the meth-
od of computing the Area of Fields from the Field
Notes, by Mathematical Tables, without the necessity
of plotting the Field. To this Section is added a use.
ful Problem for ascertaining the true Area of a Field
which has been measured by a Chain too long or too

Part second treats of laying out Land in various shapes.

Part third contains sundry Problems and Rules for dividing Land and determining the true Course and Distance of dividing Lines, or from one part of a Field to another. To this are added some observations réspecting the Variation of the Compass and the Attraction of the Needle; with Rules for finding the Variation of the Compass and for drawing a Meridian Line.

The Mathematical Tables are, A Traverse Table or Table of Difference of Latitude and Departure, calculated for every Degree and quarter of a Degree, and for any distance up to 50; a Table of Logarithms comprised in four pages, yet sufficiently extensive for common use ; a Table of Logarithmic or Artificial Sines, Tangents and Sesants, calculated for every 5 Minutes of a Degree ; and a Table of Natural Sines calculated for every Minute. To these Tables are prefixed particular explanations of the manner of using them.

GEOMETRY.

EOMETRY is a Science which treats of the properties of Magnitude.

PART I.

Geometrical Definitions. 1. A Point is a small Dot; or, Mathematically con . sidered, is that which has no parts, being of itself indivisible.

2. A Line has length but no breadth.

3. A Superficies or Surface, called also Area, has length and breadth, but no thickness.

4. A Solid has length, breadth and thickness.

5. A Right Line is the shortest that can be drawn between two Points.

6. The inclination of two Lines meeting one another, or the opening between them, is called an Angle. Thus at B. PLATE I. Figure 1. is an Angle, formed by the meeting of the Lines AB and BC.

7. If a Right Line CD. Fig. 2. fall upon another Right Line AB, so as to incline to neither side, but make the Angles on each side equal, then those Angles are called Right Angles ; and the Line CD is said to be Perpendicular to the other Line.

8. An Obtuse Angle is greater than a Right Angle; as ADE. Fig. 3.